Credibility of Confidence Sets in Nonstandard Econometric Problems
针对非标准计量问题中置信区间可能不合理（如为空或过短）的现象，提出用“赌局检验”概念衡量其可信度，并构造了通过赌局检验的置信集，应用于弱工具变量、近单位根和矩不等式等问题。
Confidence intervals are commonly used to describe parameter uncertainty. In nonstandard problems, however, their frequentist coverage property does not guarantee that they do so in a reasonable fashion. For instance, confidence intervals may be empty or extremely short with positive probability, even if they are based on inverting powerful tests. We apply a betting framework and a notion of bet-proofness to formalize the “reasonableness” of confidence intervals as descriptions of parameter uncertainty, and use it for two purposes. First, we quantify the violations of bet-proofness for previously suggested confidence intervals in nonstandard problems. Second, we derive alternative confidence sets that are bet-proof by construction. We apply our framework to several nonstandard problems involving weak instruments, near unit roots, and moment inequalities. We find that previously suggested confidence intervals are not bet-proof, and numerically determine alternative bet-proof confidence sets.